arXiv subjects

P. Helander

Publications and source records attributed to P. Helander.

At least 19 recordsLinked to original sources

arXiv2026

Second stability region for gyrokinetics and the L-H transition

Using a simple circular tokamak geometry, we show the well-known `second stability region' of MHD-ballooning modes exists for linear gyrokinetics too -- whether electrostatic or electromagnetic -- and we suggest that the plasma enters this region in H-mode as a consequence of the bootstrap current and Shafranov shift altering the magnetic field, which may occur if the normalised pressure gradient is $\alpha_{\rm MHD} \simgt 1$ and collisionality is low. By performing simulations in more realistic magnetic geometries, we demonstrate a large reduction in collisionless, electrostatic turbulent transport when going from density and temperature profiles typical of L- and H-mode, respectively. This reduction is shown to be a consequence of both the bootstrap current lowering the global magnetic shear, and the pressure gradient altering the local magnetic shear, pushing the plasma towards the second-stability region. A path connecting the L- and H-mode equilibria is constructed, along which the energy and particle fluxes exhibit non-monotonic behaviour as a function of the pressure gradient.

physics.plasm-ph↗

arXiv2025

Enhanced performance in quasi-isodynamic max-$J$ stellarators with a turbulent particle pinch

Recent stellarator reactor designs demonstrate mostly outward turbulent particle transport, which, without advanced fueling technology, inhibits the formation of density gradients needed for confinement. We introduce ``SQuID-$\tau$'', a self-fueling quasi-isodynamic stellarator capable of sustaining density peaking through inward particle transport caused by turbulence. Temperature and density profile predictions based on high-fidelity gyrokinetic simulations demonstrate enhanced performance, significantly relaxing constraints on the size and magnetic field strength for reactor designs.

physics.plasm-ph↗

arXiv2024

The effect of plasmoid drifts on the pellet rocket effect in magnetic confinement fusion plasmas

We detail here a semi-analytical model for the pellet rocket effect, which describes the acceleration of pellets in a fusion plasma due to asymmetries in the heat flux reaching the pellet surface and the corresponding ablation rate. This effect was shown in experiments to significantly modify the pellet trajectory, and projections for reactor scale devices indicate that it may severely limit the effectiveness of pellet injection methods. We account for asymmetries stemming both from plasma parameter gradients and an asymmetric plasmoid shielding caused by the drift of the ionized pellet cloud. For high temperature, reactor relevant scenarios, we find a wide range of initial pellet sizes and speeds where the rocket effect severely limits the penetration depth of the pellet. In these cases, the plasma parameter profile variations dominate the rocket effect. We find that for small and fast pellets, where the rocket effect is less pronounced, plasmoid shielding induced asymmetries dominate.

physics.plasm-ph↗

arXiv2024

Available energy of plasmas with small fluctuations

The available energy of a plasma is defined as the maximum amount by which the plasma energy can be lowered by volume-preserving rearrangements in phase space, a so-called Gardner re-stacking. A general expression is derived for the available energy of a nearly homogeneous plasma and is shown to be closely related to the Helmholtz free energy, which it can never exceed. A number of explicit examples are given.

physics.plasm-ph↗

arXiv2023

The maximum-$J$ property in quasi-isodynamic stellarators

Some stellarators tend to benefit from favourable average magnetic curvature for trapped particles when the plasma pressure is sufficiently high. This so-called maximum-$J$-property has several positive implications such as good fast-particle confinement, magnetohydrodynamic stability, and suppression of certain trapped-particle instabilities. This property cannot be attained in quasisymmetric stellarators, in which deeply trapped particles experience average bad curvature and therefore precess in the diamagnetic direction close to the magnetic axis. However, quasi-isodynamic stellarators offer greater flexibility and allow the average curvature to be favourable and the precession to be reversed. We find that it is possible to design such stellarators so that the maximum-$J$ condition is satisfied for the great majority of all particles, even when the plasma pressure vanishes. The qualitative properties of such a stellarator field can be derived analytically by examining the most deeply and the most shallowly trapped particles, although some small fraction of the latter will inevitably not behave as desired. However, through numerical optimisation, we construct a vacuum field in which 99.6% of all trapped particles satisfy the maximum-$J$ condition.

physics.plasm-ph↗

arXiv2023

Ion temperature and density gradient driven instabilities and turbulence in Wendelstein 7-X close to the stability threshold

Electrostatic gyrokinetic instabilities and turbulence in the Wendelstein 7-X stellarator are studied. Particular attention is paid to the ion-temperature-gradient (ITG) instability and its character close to marginal stability [Floquet-type turbulence (Zocco et al. 2022) with no electron temperature gradient]. The flux-tube version of the $\delta$f code stella (Barnes et al. 2019) is used to run linear and nonlinear gyrokinetic simulations with kinetic electrons. The nature of the dominant instability depends on the wavelength perpendicular to the magnetic field, and the results are conveniently displayed in stability diagrams that take this dependence into account. This approach highlights the presence of universal instabilities, which are less unstable but have longer wavelengths than other modes. A quasi-linear estimate of the heat flux suggests they are relevant for transport. Close to the stability threshold, the linear eigenmodes and turbulence form highly extended structures along the computational domain if the magnetic shear is small. Numerical experiments and diagnostics are undertaken to assess the resulting radial localisation of the turbulence, which affects the interaction of the latter with zonal flows. Increasing the amplitude of the magnetic shear (e.g. through current drive) has a stabilising effect on the turbulence and thus reduces the nonlinear energy transport.

physics.plasm-ph↗

arXiv2023

The residual flow in well-optimized stellarators

The gyrokinetic theory of the residual flow, in the electrostatic limit, is revisited, with optimized stellarators in mind. We consider general initial conditions for the problem, and identify cases that lead to a non-zonal residual electrostatic potential, i.e. one having a significant component that varies within a flux surface. We investigate the behavior of the ``intermediate residual'' in stellarators, a measure of the flow that remains after geodesic acoustic modes have damped away, but before the action of the slower damping that is caused by unconfined particle orbits. The case of a quasi-isodynamic stellarator is identified as having a particularly large such residual, owing to the small orbit width achieved by optimization.

physics.plasm-ph↗

arXiv2023

Available energy of trapped electrons in Miller tokamak equilibria

Available energy (\AE{}), which quantifies the maximum amount of thermal energy that may be liberated and converted into instabilities and turbulence, has shown to be a useful metric for predicting saturated energy fluxes in trapped-electron-mode-driven turbulence. Here, we calculate and investigate the \AE{} in the analytical tokamak equilibria introduced by \citet{Miller1998NoncircularModel}. The \AE{} of trapped electrons reproduces various trends also observed in experiments; negative shear, increasing Shafranov shift, vertical elongation, and negative triangularity can all be stabilising, as indicated by a reduction in \AE{}, although it is strongly dependent on the chosen equilibrium. Comparing \AE{} with saturated energy flux estimates from the \textsc{tglf} model, we find fairly good correspondence, showcasing that \AE{} can be useful to predict trends. We go on to investigate \AE{} and find that negative triangularity is especially beneficial in vertically elongated configurations with positive shear or low gradients. We furthermore extract a gradient threshold-like quantity from \AE{} and find that it behaves similarly to gyrokinetic gradient thresholds: it tends to increase linearly with magnetic shear, and negative triangularity leads to an especially high threshold. We next optimise the device geometry for minimal \AE{} and find that the optimum is strongly dependent on equilibrium parameters, e.g. magnetic shear or pressure gradient. Investigating the competing effects of increasing the density gradient, the pressure gradient, and decreasing the shear, we find regimes that have steep gradients yet low \AE{}, and that such a regime is inaccessible in negative-triangularity tokamaks.

physics.plasm-ph↗

arXiv2023

Bounce-averaged drifts: Equivalent definitions, numerical implementations, and example cases

In this article we provide various analytical and numerical methods for calculating the average drift of magnetically trapped particles across field lines in complex geometries, and we compare these methods against each other. To evaluate bounce-integrals, we introduce a generalisation of the trapezoidal rule which is able to circumvent integrable singularities. We contrast this method with more standard quadrature methods in a parabolic magnetic well and find that the computational cost is significantly lower for the trapezoidal method, though at the cost of accuracy. With numerical routines in place, we next investigate conditions on particles which cross the computational boundary, and we find that important differences arise for particles affected by this boundary, which can depend on the specific implementation of the calculation. Finally, we investigate the bounce-averaged drifts in the optimized stellarator NCSX. From investigating the drifts, one can readily deduce important properties, such as what subset of particles can drive trapped-particle modes, and in what regions radial drifts are most deleterious to the stability of such modes.

physics.plasm-ph↗

arXiv2023

Drift of ablated material after pellet injection in a tokamak

Pellet injection is used for fuelling and controlling discharges in tokamaks, and it is foreseen in ITER. During pellet injection, a movement of the ablated material towards the low-field side (or outward major radius direction) occurs because of the inhomogeneity of the magnetic field. Due to the complexity of the theoretical models, computer codes developed to simulate the cross-field drift are computationally expensive. Here, we present a one-dimensional semi-analytical model for the radial displacement of ablated material after pellet injection, taking into account both the Alfv\'en and ohmic currents which short-circuit the charge separation creating the drift. The model is suitable for rapid calculation of the radial drift displacement, and can be useful for e.g. modelling of disruption mitigation via pellet injection.

physics.plasm-ph↗

arXiv2023

Energetic bounds on gyrokinetic instabilities. Part III. Generalized free energy

Free energy, widely used as a measure of turbulence intensity in weakly collisional plasmas, has been recently found to be a suitable basis to describe both linear and nonlinear growth in a wide class gyrokinetic systems. The simplicity afforded by this approach is accompanied by some drawbacks, notably the lack of any explicit treatment of wave-particle effects, which makes the theory unable to describe things like stability thresholds or dependence on the geometry of the background magnetic field. As a step toward overcoming these limitations, we propose an extension of the theory based on a generalization of free energy. With this it is demonstrated that resonance effects are recovered, and the bounds on growth are significantly reduced. The simplicity and efficient computation of the associated "optimal" growth rates makes the theory potentially applicable to stellarator optimization.

physics.plasm-ph↗

arXiv2022

A single-field-period quasi-isodynamic stellarator

A single-field-period quasi-isodynamic stellarator configuration is presented. This configuration, which resembles a twisted strip, is obtained by the method of direct construction, that is, it is found via an expansion in the distance from the magnetic axis. Its discovery, however, relied on an additional step involving numerical optimization, performed within the space of near-axis configurations defined by a set of adjustable magnetic-field parameters. This optimization, completed in 30 seconds on a single cpu core using the SIMSOPT code, yields a solution with excellent confinement, as measured by the conventional figure of merit for neoclassical transport, effective ripple, at a modest aspect ratio of eight. The optimization parameters that led to this configuration are described, its confinement properties are assessed, and a set of magnetic-field coils is found. The resulting transport at low collisionality is much smaller than that of W7-X, and the device needs significantly fewer coils thanks to the reduced number of field periods.

physics.plasm-ph↗

arXiv2021

Energetic bounds on gyrokinetic instabilities. Part I: Fundamentals

Upper bounds on the growth of free energy in gyrokinetics are derived. These bounds apply to all local gyrokinetic instabilities in the geometry of a flux tube, i.e. a slender volume of plasma aligned with the magnetic field, regardless of the geometry of field, the number of particle species, or collisions. The results apply both to linear instabilities and to the nonlinear growth of finite-amplitude fluctuations.

physics.plasm-ph↗

arXiv2021

The available energy of trapped electrons and its relation to turbulent transport

A collisionless plasma possesses a certain amount of "available energy", which is that part of the thermal energy that can be converted into field energy. Here, a calculation is presented of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarator and a tokamak. The numerical calculation of available energy is extremely fast and shows a strong correlation with the turbulent energy fluxes found in the gyrokinetic simulations. Indeed, the energy flux is found to be proportional to the available energy to the power of approximately 3/2, as one would expect from a simple phenomenological model.

physics.plasm-ph↗

arXiv2021

Upper bounds on gyrokinetic instabilities

A family of rigorous upper bounds on the growth rate of local gyrokinetic instabilities in magnetized plasmas is derived from the evolution equation for the Helmholtz free energy. These bounds hold for both electrostatic and electromagnetic instabilities, regardless of the number of particle species, their collision frequency, and the geometry of the magnetic field. A large number of results that have earlier been derived in special cases and observed in numerical simulations are thus brought into a unifying framework. These bounds apply not only to linear instabilities but also imply an upper limit to the nonlinear growth of the free energy.

physics.plasm-ph↗

arXiv2020

Available Energy from Diffusive and Reversible Phase Space Rearrangements

Rearranging the six-dimensional phase space of particles in plasma can release energy. The rearrangement may happen through the application of electric and magnetic fields, subject to various constraints. The maximum energy that can be released through a rearrangement of a distribution of particles can be called its available or free energy. Rearrangement subject to phase space volume conservation leads to the classic Gardner free energy. Less free energy is available when constraints are applied, such as respecting conserved quantities. Also, less energy is available if particles can only be diffused in phase-space from regions of high phase-space density to regions of lower phase-space density. The least amount of free energy is available if particles can only be diffused in phase space, while conserved quantities still need to be respected.

physics.plasm-ph↗

arXiv2020

Suppression of turbulence by trapped electrons in optimised stellarators

In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the "trapped electron mode" (TEM) is stabilised if specific optimisation criteria are satisfied, as in the Wendelstein 7-X experiment (W7-X). Here we find, by numerical simulation, that W7-X indeed has low TEM-driven transport, and also benefits from stabilisation of the ion-temperature-gradient mode, giving theoretical support for the existence of enhanced confinement regimes at finite density gradients.

physics.plasm-ph↗

arXiv2019

Effect of plasma elongation on current dynamics during tokamak disruptions

Plasma terminating disruptions in tokamaks may result in relativistic runaway electron beams with potentially serious consequences for future devices with large plasma currents. In this paper we investigate the effect of plasma elongation on the coupled dynamics of runaway generation and resistive diffusion of the electric field. We find that elongated plasmas are less likely to produce large runaway currents, partly due to the lower induced electric fields associated with larger plasmas, and partly due to direct shaping effects, which mainly lead to a reduction in the runaway avalanche gain.

physics.plasm-ph↗